Apparatus for broad-band radio transmission



Jan. 15, 1952 R POUND 2,582,604

APPARATUS FOR BROAD-BAND RADIO\TRANSMISSI ON Original Filed Feb. s, 1943 '5 Sheets-Sheed 1 2 1 I3 I F|G.3

II I Y T I iNVENTOR ROBERT v. POUND ATTORNEY Jari. 15, 1952 R POUND 2,582,604

APPARATUS FOR BROAD-BAND RADIO TRANSMISSION Original Filed Feb. 8, 1943 5 Sheets-Sheet 2 INVENTOR w ROBERT v. POUND ATTORN EY FIG. l2

n- 1952 R. v. POUND 2,582,604

APPARATUS FOR BROAD-BAND RADIO TRANSMISSION Original Filed Feb. 8, 1943 5 Sheets-Sheet 3 FIG.I3 F|G.I6

6! 6! l6 If I FIG. l5

-INVENTOR" ROBERT v. POUND ATTORN EY Jan. 15, 1952 v, POUND 2,582,604

APPARATUS FOR BROAD-BAND RADIO TRANSMISSION original Filed Feb. 8, 1943 5 Sheets-Sheet 4 FIG. l9

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I FIG.23 z z I FIG. 22-8 1 z INVENTOR I ROBERT V. POUND Z5 Fl6.22-0 BY W4,

ATTORNEY 7 R. v. POUND APPARATUS FOR BROAD-BAND RADIO TRANSMISSION Jan. 15, 1952 5 Sheets-Sheet 5 Original Filed Feb. 8, 1943 FIG. 26

FlG.28-A

FlG.28-B

FIG. 28 -C FIG. 30

INVENTOR ROBERT v. POUND FIG.29

ATTORNEY Patented Jan. 15, 1952 2,582,604 APPARATUS FOR BROAD-BAND RADIO TRANSMISSION Robert V. Pound, Cambridge, Mass, assignor, by mesne assignments, to the United States of America as represented by the Secretary of the Original application February 8, 1943, Serial No.

. a predetermined small amplitude. Since the twoconductor transmission lines generally used with stub supports are almost invariably of the coaxial conductor type the invention in its most practical aspectsrelates to coaxial conductor transmission lines chiefly.

High-frequency transmission lines supported by short-circuited quarter-wave stub lines are for many reasons preferred over, insulator-spaced transmission lines A transitory fiashover in an insulator-supported line. is likely to cause permanent damage to the insulators, thereby enharmingthe probability of further breakdown,

whereas in a stub-supported line, a transitory flashover will usually leave the line in as good condition as before. ,The use of stub-supported lines has heretofore been complicated by the fact that. the. stubsupport is usually completely effective only for a given frequency and that reflections are set up at other frequencies which are quite considerable even with a small difference'between the frequency of operation and the design frequency. Frequency-sensitivity arising from the association of a resonant element or structure with some kind of transmission means is also a problem in apparatus other than stubsupported coaxial conductor lines.

It is an object of this invention to provide means for counteracting the frequency-sensitivity of resonant elements associated with transmission lines and the like and for producing thereby a combined structure which will permit the transmission of electrical oscillatory energy over a relatively wide range of frequencies. It is a particular object'of this invention to provide stub supports for a transmissionline which will permit the transmission of a range or band of frequencies with little or no reflections and which may. readily be provided in a form suitable for the construction of coaxial conductor transmission lines. It is a further special object of this invention to provide a stub support of such form that transmission of a range of frequencies with little or no reflections and little or no atten uation may be effected even though only a single stub support or an odd number of stub supports are" used in uie' rapsmission line in' question; Other objects of this invention'will be apparent Divided and this application August 7 I 10,1948, SerialNo. 43,526

from the following description of the invention.

The eifect of quarter-wave stub supports upon the frequency transmission characteristic of a two-conductor transmission line with which said stub supports are associated may be referred to as frequency-sensitivity. If at the design frequency the supporting stubs have zero susceptance, then, at lower frequencies, for which the stubs will be less than a quarter-wave long, these stubs will have an inductive susceptance and will set up the corresponding type of energy reflecticn where they connect with the transmission line. Likewise, at higher frequencies, for which the stubs are more than a quarter wave long, these stubs will have a capacitive susceptance and will set up a corresponding type of reflection where they connect with the transmission line. In the principalform of thepresent invention, in order essentially to neutralize the aforesaid frequency-sensitivity over a range of frequencies in the neighborhood of the design frequency, there are associated with each stub two transformers, one on, each side of the stub, which transformers may, and preferably do, form a single structure with its center at the location of the stub. These transformers are sections of transmission line of a length substantially equal to an odd number of quarter-wave lengths, preferably a single quarter-wave length, and having a characteristic admittance difierentf'rom that of the rest of the transmission line. In the preferred case, where the two transformers unite to form a single structure, as well as in certain other cases, the characteristic admittance of the sec-' tion of line which constitutes the transformer is. greater than that of the main portions of the transmission line. Such transformers may be readily constructed by varying the relative diameters of the conductor of a coaxial conductor transmission line for the desired length of line. This is most conveniently done by enlarging or reducing the diameter, as the case may be, of the inner conductor of such a transmission line.

The invention will be more fully explained with reference to the annexed drawings, in which:

Fig. 1 is a longitudinal view, mostly in section; or one form of supporting stub for a coaxial conductor transmission line in accordance with the present invention;

Fig. 2 is a sectional view of the structures of Fig. 1 along the line 2-2 of Fig. 1;

Fig. 3' is a sectional view of the structure of Fig. I along the line 3+3 of Fig. 1;

Figs. 4, 5, 6, 7, 8, 9, and 11 are theoretical diagrams for the purpose of explaining the be havior of stub supports constructed in acc0rdance with the present invention;

Fig. 10 is a longitudinal view, chiefly in' section, showing another form of supporting stub and its associated transformers in accordance with the present invention;

Fig. 12 is a longitudinal view of still another form of supporting stub and associated transformer in accordance with the present invention;

Fig. 13 shows a form of double stub support as constructed in accordance with the present invention;

Fig. 14 illustrates the application of the present invention to a T-junction connecting a transmission line to a side branch which is adapted to be short circuited during transmission at high power levels along the said transmission line;

Fig. 15 is a longitudinal view, partly in section, of a form of stub support for a coaxial conductor transmission line which is adapted to be used either as a straight through or as a right ang l-e support;

- Fig. 16 is a partly sectional view of the apparatus shown in Fig. 15 along the line |6l6 of Fig. 15;

Figs. 17 and 18 are theoretical diagrams illustrating the behavior of the form of the invention shown in Figs. 15 and 16;

Fig. 19 is a. theoretical diagram illustrating relations simplified in certain other diagrams;

Fig. 20 is a sectional view of another form of apparatus embodying the present invention and Figs. 21 and 21A are theoretical diagrams relating thereto;

Fig. 22 is a sectional view of still another form of apparatus embodying the present invention andFigs. 22A, 22B and 220 are theoretical diagrams relating thereto;

Fig. 23 is a sectional view of still another form of apparatus embodying the present invention and Fig. 24 is a theoretical diagram relating thereto;

Fig. 25 is a diagrammatic perspective view of a form of apparatus embodying the present invention and employing hollow pipe wave guides, and Fig. 26 is a theoretical diagram relating thereto;

Fig. 27 is a diagrammatic perspective view of another form of apparatus embodying the present invention and also comprising hollow pipe wave guides;

Figs. 28 and 29 illustrate, in cross section, forms of apparatus realizing a partial accomplishment of the purposes of the invention;

. Figs. 28A, 28B and 280 are theoretical diagrams relating to the apparatus of Fig. 28 and Fig. 30 is a theoretical diagram relating to the apparatus of Fig. 29.

In Figs. 1, 2, and 3 is shown a coaxial conductor transmission line having an inner conductor 6 and an outer conductor 1, the ends of the transmission lines being broken away in Figs. 1 and 3 for convenience of illustration. A stub support consisting of the section of transmission line 8 havingan inner conductor 9 and an outer conductor l0 connected by a short-circuiting plug serves to maintain the conductor 6 in fixed relation to the conductor 1. The conductors 6 and 9 are drilled and tapped to receive a threaded stud I2, which may be of steel or brass, for the purpose of permitting convenient assembly of the stub. Since very little current flows in and out of the stub where it connects with the transmis sion line, a soldered joint is not necessary at this point. Good electrical contact is, however, desirable betweenthe plug II and the conductors 9 and 10, so that the plug l I is preferably soldered to the said conductors;

1n the neighborhood of the stub line 8, the diameter of the conductor 6 is enlarged for a total length of approximately a half-wave length for the frequencies desired to be transmitted. This enlargement of the diameter of the conductor 6, which constitutes a pair of quarter-wave transformers on each side of the center of the stub between the stub and the transmission line 5, may be conveniently provided by a close fitting sleeve l3 mounted on the conductor 6 and preferably soldered thereto at least at its ends.

The function of the arrangement shown in Figs. 1, 2, and 3 and the manner in which the important dimensions are related will be understood from a consideration of the theoretical diagrams of Figs. 4-9, inclusive. Referring to these figures, the line YY represents the real axis of an admit tance diagram, the point Yo indicates the characteristic admittance of the transmission line 5 mittance of the transmission line constituted by the transformer, which is to say of the transmission line composed of the conductor 13 as inner conductor and the conductor 1 as outer conductor (Fig. 1). It is desired, in order that transmission may be achieved along the line 5 past the P stub 8 without substantial reflections, that when the line 5 is properly terminated and, therefore,- presents the admittance Y0 when looking awayfrom the stub from beyond the matching transformer, it should also present the same admittance Y0 when seen through the matching transformer and stub.

Let it be assumed that at the point IS on Fig.

1 the portion of the line 5 extending downward therefrom presents an admittance of Y0. Since the characteristic admittance of the transformer is Y1, the admittance at various points farther along the first quarter-wave length of the stub to the first quarter-wave length of the transformer which is to say between the location l5 and the axis of the stub 8 will then be represented by an arc 180 long, so that the admittance at the axis of the stub, disregarding for the moment the f effect of the stub, will be represented by the point A on Fig. 4, which, since it lies on the real axis, has no imaginary (susceptance) components. Let it now be assumed that the stub has an electrical length of a quarter-wave length for the frequency in question. therefore, the stub will have a zero susceptance, and if conductive losses are neglected, which may be done for practical purposes, it will present 'likewise zero conductance, so that the effect of the stub upon the admittance at the center of the transformer is zero for the frequency now under consideration. The admittanc at points along the transformer between the axis of the stub and the upper end of the transformer may then be represented by another semi-circle beginning at.

between thelocation l 5 at the bottomend ofthe At such a frequency,

transformer and the axis of the stub willbe less than 180"long, and likewise-, at frequencies lower than that at which the stub has an electrical lengthof a quarter-wave length, the stub will provide aninductive susceptance across the line (more exactly speaking, across the transformer) There will generally be some frequency lower than that for which the conditions of Fig. 4 obtain' at which the two'effects just mentioned will exactly counteract each other, as shown in Fig. 5. In Fig 5 it is seen that at some frequency the admittance at the axis of the stub when measured in the absence of the stub will be represented by apoint E The effect of the stub, which is that of adding an inductive susoeptance, may then be represented by a downwardly directed vertical line B'C. When the effect of the other half of the transformer is added in by the circular arc beginningat C, it is seen that the admittance presented at the top of the transformer again Yo.

The effect of the transformer and the admittance of the stub do not change in the same manner with respect to frequency, although the manner in which these effects change with fre-- quency, in the range between the frequency for which the conditions of Fig. 4 obtain and the" frequency for which the conditions just illustrated with respectto Fig. 5 obtain differ only slightly. For intermediate frequencies in this range, the admittance looking down the line 5 through the transformer and stub will not be appreciably different from Yo (this has been confirmed by experiments). For some frequency substantially lower than that corresponding to the diagram YoBC of Fig. 5, however, a different situation will generally prevail, as shown on Fig. 5 with the assistance of the dotted line B'C. The'effect of the first half of the transformer will then be represented by the arc YoB', the effect of the stub will be represented by the vertical line 3'0 and the effect of the second half of the transformer will be represented by the arc C'Ya, Ya being the admittance looking down the line through the transformer and past the stub. Ya being appreciably different from Yo; reflections will occur when it is sought to transmit energy at the frequency in question in the-line 5.

In general, the effects of the stubv and of the transformer arrangements will exactly counteract each other at a frequency higher than that for which the conditions of Fig. 4 obtain as well as'at a frequency lower than the said frequency. The higher frequency case is illustrated in Fig. 6. In this case the effect of the first half of the transformer will be represented by the arc YoD, which is more than 180 inlength. The frequency being higher than thatfor which they stub is an electrical quarter-wave length long, the stub will present a capacitive suscep-tance, which is indicated on Fig. 6 by the upwardly directed vertical line DE. The effect of the second half of the transformer will then be shown by the arc EYo, which like the arc YoD ismore than 180", both these arcs being ,of the same: length in degrees on account of the symmetrical arrangement of the. transformer. For some frequency considerably higher than that just considered the effect of the first half of the transformer will be represented by the arc. YoD, the; effect of the, stub by the vertical line DE'v and the effect of the second half of the trans-- former by the arc E'Yb.

Yb being appreciably. difierent from Yo,v reflections. will occur: at; this;

frequency, while for th diagram YoDEYo applied, the'input admittance of the system was exactly Yo, so that at that frequency no reflections would occur.

The three frequencies represented respectively by the situation shown in Fig. 4,- thesituation shown by the diagram YOBC-Ytl of'Fig. 5 and the situation shown by the diagram YoDEYo of Fig.

6 (which frequencies may be spoken of as the resonant frequenciesof the system, the system being in asense a band-pass filter) may be made to be closer together or farther apartby cone:

the circle shown in Figs. l, 5, and 6, thereby in creasing the effect of the transformer for a given change in frequency. The range within which the distance of the points B, D, etc., from the axis YY' varies linearly with frequency with be extended to larger values of susceptance. which will tend to increase the band-width, particularly if the effect of the stub is approximately linear within such range.

Decreasing the characteristic admittance of the stub 8 will tend to increase the separation between the resonant frequencies as above de-- fined, but at the same time, if carried too far, this may result in increasing the amount of reflections for frequencies lying between. these resonant frequencies. Since in the formof apparatus herein described no measurable reflec--' tions have been detected within the pass bands of the respective devices, itfollows that the characteristic admittance may be considerably re-' duced without introducing an undesirable amount of reflections. In practice it is convenient to make the characteristic admittance of the stub line 8 the same as the characteristic admittance of the line 5 forthe convenience of construction that results from using tubing and rods of the same diameter as are used for the main part of the transmission line. The efi'ectof the variation of the characteristic admittance of the stub 8 may be understood by considering the fact that the susceptance of the stub 8 as" it appears across the line 5' varies with fre quency as a trigonometric tangent function in which the characteristic admittanceappears as a multiplying factor.- The susceptance component-of the admittance represented by points suchas the pointB' and the point: D in Figs15- and 6 respectively, as the frequency is changed,- varies as a function which is substantially linear in the neighborhood ofthe frequency for whichthe transformer is a half-wave length long-and which has a curvature opposite to that of the tangent function as the frequency is either raised or lowered. For certain values of the characteristic admittance of the stub 8, the slopes of the tangent function and of the function corresponding to the susceptance necessary to neutralize the effect of the transformer at various frequencies will be almost the same and the three resonant frequencies will lie close together or even coincide. For smaller values of the characteristic admittance of the stub 8 the curves will cross at larger angles at the middle resonant frequency and the resonant frequencies will lie farther apart.

In the actual practice of the inventiomcn additional small. but appreciable effect is to'bem e frequency for which the ausaeos.

observed which should be taken into account in order to obtain the best results possible in accordance with the present invention. This efiect requires a small modification of the foregoing description of the operation of the stub support.

The discontinuity caused by the sudden change of the diameter ofv the inner conductor 6 at the ends of the transformer appears to add a small capacitive susceptance at each end of the transformer. This effect maybe compensated for by either lengthening the stub line 8 or shortening the transformer. In other words, the length of the, stub line is to be lengthened relative to the length of the transformer. The frequency for which the transformer is a half-wave length long and the frequency for which the stub-is a quarter-wave length long then no longer coincide. Under these conditions the middle resonant frequency of the structure may be made to coincide with the frequency for which the stub is. electrically a quarter-wave length long, or it may be made the frequency for which the transformer is a half-wave length long or it may be made some other frequency, such as a frequency between the aforesaid frequencies. The first of these cases corresponds to Fig. '7, the second corresponds to Fig. 8 and the third corresponds to Fig. 9. In these three figures the capacitive effect of the discontinuity at one end of the transformer is shown by the vertical line YUP and the capacitive of the discontinuity at the other end of the transformer is shown by the vertical line QYo. Referring to Fig. 7, which illustrates the case where the middle resonant frequency is that for which the stub is electrically a quarter-wave length long, the effect ofthe first half of the transformer, which for the frequency in question is less than a quarter-wave length, is represented by the arc PA. The stub adds nothing at this frequency and its effect, therefore, does not appear on the diagram. The effect of the other half of the transformer is shown by the arc AQ, which is of the same length and radius as the arc PA. Addition of the susceptance QYo then shows that the impedance looking down the line through the transformer andpast the stub is Yo, as desired.

In the situation iliustrated Fig. 8, the stub at the middle resonant frequency has the capacitive susceptance RS which is equal to the sum of the susceptances YOP and QYo. The arcs PR and SQ, which correspond to the respective effect of the two halves of the transformer, will then be 180 long, thus indicating that at this frequency the total transformer length is a half-wave length.

In the situation shown in Fig. 9, the effect of the first half of the transformer is shown by the arc PR, which is less than 180, and the effect of the stub is shown by the vertical line RS', which is somewhat shorter than the.line QP. The effect of the second half of the transformer is represented by the arc S'Q. This diagram, therefore, represents the case in which the resonant frequency in question is at a frequency between the frequency for which the stub is electrically a quarter-wave length and the frequency for which the transformer is a half-wave length.

In practice the relation between the physical length of the stub line and its electrical length as observed from its electrical behavior is not usually amenable to convenient exact theoretical prediction, at least in the case where the diameter of the line is an appreciable fraction of the wave length, such as wave length or more. The

non-uniformity in the configuration of the stubline where it joins the main transmission line requires an estimation of the so-called end effect in order to predict the relation of the length of the stub line, as measured from a given point of the junction, to the electrical length of the line. For example, in a coaxial conductor line of a characteristic impedance of 48 ohms in which the inner diameter of the outer conductor is approximately 0.22 wave length, the physical length, measured from the axis of the main line to the terminating conducting surface of the stub, of a stub having an electrical length of a quarter-wave length, is equal t approximately 0.35 times the normal wave length (this applies to a case where no transformer is associated with this stub). It is possible that the presence of the transformer at the junction of the stub and the main line may have an added effect upon this end effect, since the transformer changes the 'configuration of the junction. Because of the involved nature of the relation between the physical dimensions of the stub and the electrical wave length thereof, it is convenient as a matter of design to dimension the stub and transformer structure so that the middle resonant frequency will occur in the neighborhood of the frequency for which the transformer has a length of a half-- wave lengththat is to say, the transformer is provided with a length equal to half of the wave length corresponding to the desired mid-band frequency. Because the capacitive effect of the discontinuity at the end of the transformer is small, when the stub is then adjusted for zero reflections at this frequency, the pass band may be expected to be reasonably symmetrically disposed with respect to the frequency for which the transformer is equal to a half-wave lengthin length. Since the exact location of the resonant frequencies is dificult because of the small amount of reflection occurring within the pass band, in practice the stub length is adjusted for a length which locates the pass band of the device with the desired amount of symmetry with respect to the frequency for which the transformer is equal to a half-wave length.

Illustrative dimensions for the stub and associated transformer structure shown in Figs. 1, 2, and 3, referred to the wave length, are given in the following table:

Table I [Normal wave length in air= l] The transformer arrangement shown in Fig. 1 may be used to counteract the frequency sensitivity of devices other than supporting stubs for instance, circuits of the parallel resonant type connected across the line either directly or by means of a branch line. Likewise, stubs of a length greater than the quarter wave length, such as wave length stub, may be associated with a transformer arrangement in accordance with the present invention in order to reduce frequency sensitivity. The input susceptance of a stub any odd number of quarter-wave lengths long and short-circuited at its farther end is known to be similar to that of a parallel resonant-tuned aseaem cult. Where the stub or parallel resonant etuned circuit has a greater sensitivity to frequency "changes than the simple quarter "wave :Sllllb support, as might, for instance, be the case with -'a :stub of a'wave length long, .it may :-be desirable, in order to maintain a wide bandwidth, to increase the frequency-sensitivity of the compensating transformer arrangement by either increasing the thickness of the "sleeve 13 or else using a sleeve with a total length of three halfwave lengths. Thus, .as previously mentioned, in order to obtain results such as those above described, the transformers on each side of the :stub may, in general case, be any odd number of quarter-wave lengths long, provided they are both of the same length. "If :these transformers are both made "to be of a wave length long, the total transformer lengths will be three halfwave lengths.

Referring to the diagram of Figs. 4, 5, and 6, whereas increasing the thickness of the sleeve I 3 increases the radius of the circles drawn about Y1 and passing through Yo, lengthening the sleeve to a length of approximately 11/ wave lengths does not vary the radius but increases the displacement of points such as B and D along the circumference of the circle for a given change in frequency.

It should be noted at this point that the circle diagrams in the drawings have been greatly simplified in order to clarify the principles of the invention. It is to :be understood that although "a semi-circular'arc such as the arc YoA of Fig. 4 corresponds exactly to 90 electrical de- -grees, withinsuch 'sem'icircle there is no fixed proportionality between degrees of arcs and electrical degrees, the electrical degrees being crowd-' ed together in the left hand quadrants and being spread apart in the right hand quadrants. This distinction is of relatively small importance in the above considered instances, although it "will be seen to have'some bearing on other cases hereinafter treated. Another feature of the circle diagram for the calculation of admittances which has been neglected for purposes of simplicity is the fact that the family of circles relating to a point Y1 is not a family of concentric circles drawn about Y1, but a family of circles draw-1 about points to the rightof Y1 which approach Y1 as the radius of the circles decreases. In order "about the'circumference of the circles.

'It "will be seen that the sixty degrees of are near the right hand intersection with the real axis includes a greater number'of electrical degrees for the smaller circle than for the larger "circle. This would seem to indicate that a total transformer length with a smaller transformer radius would be more desirable than a total transformer length with a-greater transformer radius. points B and C for a The points corresponding to the 10 transformer, however, would move around the circumference of the circle at three times the vrate that the points B and C move for the transformer, for a given rate ofchange of X, .so that this respect the transformer would appear to give the greater bandwidth. The latter effect is probably predominant, but since the two effects here pointed out to some extent balance each other, it maybe transformers in other cases.

The clockwise-travel around the circle and-the orientation (sense) of the inductance and :capacitance vectors is in accordance with the conventions applicable when looking toward the generator. In the devices here in -question, it makes no practical difference which way power is transferred. It is also to be notedthat although the graphical method of description is used herein because 'of its relative clarity of presentationthe :behavior of the devicescan also be derived mathematically by'known analytical methods, by which the resonant frequencies of transmission in given cases can be calculated.

Although with respect to the simplicity of construction and reliability of operation and for other reasons it is preferred in the practice of this invention to provide the quarter-wave transformers directly adjacent to the supporting-stub, so that they combine to form a single half-wave transformer, it is not necessary, in order-to take advantage of the principles of the'present invention, that this type of construction be followed.

For instance, each of these quarter-wave transformers may be moved one half-wave length away from the supporting stub in question, as shown in Fig. :10. In the arrangement shown in .Fig. 10, the quarter-wave length transformers 20 and H are so located that the distance from the axis of the stub line 8 to the nearer end of each of these transformers is substantially a half- Wave length-i. e. twice the length of one of the quarter-wave transformers. The behavior of such an arrangement is illustrated by the diagram, Fig. 11. The effect ofthe first quarterwave transformer, for instance the transformer 2|, is indicated by the arc YoWl for some frequency lower than the desired mid-band frequency, which mid-band frequency may, as previously indicated, be that for'which the transformers 20 and 2| each are a quarter-wave length long. The effect of the first half-wave length of transmission line between the first transformer and the stub 8 will then correspond to the arc of the large circle W1W2, going about the circle in a clockwise direction. Just as the =arcYoW1 was somewhat less than a semi-circle,

the arc W1W2 will be proportionately less than 'a'full circle.

Assuming now that the frequency in question is that corresponding to the lower resonant frequency of the system, the susceptance added by the stub 8 at its point of connec- Isztion with the transmission line- 5 may be repre- 1 1 sented by thefdownwardly' directed"- line W2W3. "The eflfect of the second half-wave length of line located between the stub 8 andthe second quarter-wave transformer may then be represented by the arc W3W4, being again somewhat less than a full circle. and the effect of the second quarterwave transformer, for instance the transformer 20, may then be represented by the arc W4Yo.

In this arrangement a change in frequency affeots the position of the point W2 both by short- .ening r len thening the arc YoW1 and by a similar effect on the arc.W1W2. The frequency sensitivity of the compensating transformersvstem will, therefore, tend to be greater than that of the transformer system of Fig. 1, so that for a given supporting stub the wall thickness of the sleeve mounted upon the conductor 6 to form the transformers 20 and 2! of Fig. may be thinner than: that of the sleeve l3-of Fig.1. It is to be noted in connection with Fig. 11 that the locus of points such as-jWz is not exactly a circular are but the deviation of this locus from a circular arc may be expected to have a ne ligible effect within the limits of the pass band of frequencies.

Another possible arrangement according to this invention is one similar to that of Fig. 10 but with half-wave length transformer line sections instead of the sections 20 and 2 I. with their nearer extremities in this case an odd number of Quarter-wave lengths from the .axis of the stub line. Such an arran ement of transformers would have less fre uency sensitivity than the transformer arrangement of Fig. 1c. The analysis of the behavior of such a svstem may be made by means of diagrams similar to Fig. 11. "Fromthe fore oin discussion. it follows that the whole section of transmission line between the farther ends of the transformer s ctions. in-

cluding any portion of line such as that between the sections 20 and 2|, a rs'as an admittancetr'ans'forming portion of line. It is important that the total len th of such transforming portion (i. e. twi e the distance from'the axis of the stub to either end of the transforming por- 7 -tion of line) should, in the case of transformers including portions of increased characteristic admittance, be approximately an odd number of half-wave lengths. whether the length of the sections of increased characteristic admittance is whichis not easy to calculate in a general way, the latter type of arrangements are not pre- 'ferred.

Another possible arrangement of transformers in the line'5 for compensating for the frequency sensitivity of the supporting stub 8 over a definiterange of frequencies is shown in Fig. 12. In this case the quarter-wave transformers are of the under-cut type and the distance from the xis of th st"n to the n rer e d, of eit r of these transformers is an odd number of quarter-wave lengths. which in the case of Fig. 12 is a single quarter-wave length. In Fig. 12 the "conductor 6 is provided with portions of reduced diameter which appear at 22 and 23. these reduced diameter portions of the conductor 6 cooperating with the outer conductor 1 of theline 5 to define admittance transforming sections of line. These reduced diameter portions of the conductor 6 each have a length of a quarterwave length, such quarter-wave length being re=- ferred to a frequency approximately in the middle of the desired transmission band. The frequency sensitivity of this arrangement of compensating transformers is intermediatexbetween that of the transformer arrangement of Fig. 1 and that of the transformer arrangement of Fig. 10. The behavior of the arrangement of Fig. 12 may be illustrated by theoretical-admittance diagram similar to Figs. 49 and Fig. 11 and the manner of such representation may be understood without further explanation. In such representation, the point Y1 will, of course, lie to the left of Y0 so that an arc drawn about Y1 beginning at Ya in a clockwise direction will begin downward.

Similarly to the considerations raised in connection with Fig. 10, the arrangement of transformers shown in Fig. 12 may be modified by making the sections of line having reduced characteristic admittance a half-wave length long in stead of a quarter-wave length long, provided that the total distance from the junction of the stub and the main line to the farther end of either section of reduced characteristic admittance is made to be an integral number of half-wave lengths. Indeed, the length of the sections of reduced characteristic admittance may be some length other than an integral number of quarterwave lengths, provided both such sections'are of the same length and provided that the location of said sections is correspondingly adjusted, but the latter type of arrangements are not preferred because of the more involved nature of design calculations-and because of decreased linearity of frequency-sensitivity compensation that may be expected in such cases.

As previously mentioned, the transformer arrangement of Fig. 1 is preferred for its simplicity of construction and for other reasons. The frequency sensitivity of the transformer arrangement is quite adequate, even with small sleeve thicknesses, to counteract in the desired manner the frequency sensitivity of the supporting stub. Figs. 13 and 14 show modifications of the arrangement of Fig. 1 for the application of the prime ciples of the present invention to specific prob lems more complicated than the provision of a simple stub support structure. Fig. 13 shows a symmetrical double stub support for a transmission line, such double stub support being useful for transmission lines intended to be rotated about the line axis, since the symmetry of the arrangement provides dynamic balance in the case of such rotation. In Fig. 13 the transmission line is shown at 5 and the symmetrically disposed stub supports are indicated at 25 and-2B. An enlargement of the conductor 6 is shown at 21 which'has a total length of a half-wave length for a, frequency approximately in the middle of the desired pass band, and this constitutes a pair of adiacent transformers symmetrically disposed a out the common axis of the stubsi25' and 28. As in the case of the structure of Figs..l, 2, and 3 the stubs 25 and 26 have an electrical length slightly greater than a. quarter-wave length at the frequency for which the transformer 27 is a halfwave lengtK'long', in orde'r'that'th'e capacitance effect produced at the extremities of the transformer 27 may be compensated for. The'com'- bined effect of the stubs Z5 and 26 is a greater frequency sensitivity than that produced by a things being equal, requirea greater sleeve thickness than was necessary in the case of the sleeve l3.

Fig. 14 shows the application of the present invention to the junction with the main transmission line of a branch line which isadapted to be short circuited at a suitable place when a predetermined power level is reached by the oscilla-.

tion in the main transmission li es. Such branch lines are employed in radio-echo location and detection system in which transmiss on and reception of radio waves is effected over a s n le antenna sys em fed by a single tran mission line. In Fig. 14 the main transm ssion line, wh ch in a radio-echo location and detection system would usually be the transm ssion line connecting the transmitter apparatus with the antenna, is shown at 30 and comprises an inner conductor 3! and an outer conductor 32. A branch tran mission line leading toward a short circuitin; device and eventually to the receiver is shown at 35 and'comprises an inner conductor 36 and an outer conductor 31. The branch transm ssion'line'afi meets the transmiss on line'sii at a right angle unction at wh ch iunction the inner conductors 35 and iii are sup orted with respect to the outer conductor struct re by means of a stub tran mission line Mlwhich includ s an inner conductor 4 an outer conductor 42 and a terminal short-circuit ng plug 43; The branch line 35 is terminated by a l op 45 wh ch is adapted to couple into a tun-ed electrical breakdown device throu h which the receiver input is connected to the line 35. Such coupling is elfective when the end of the lin i3 is soldered or otherwise secured and electrically connected into a suitable aperture in the walls of the sa d electrical breakdown device. When the radio frequency energy in the line 36 reaches a'predetermined amplitude, an electrical breakdown will occur in the breakdown device int which the loop 45 is coupled. The breakdo n of the electrical breakdown. device will so be tuned to'said device as to produce a very low impedance coupled electromagnetically to the loop 45. so that the loop 45, except for a certain amount of inductive loading, which is commensurate'with "the amount of loading produced by the loop the a sence of any neighboring resonator 0r breakdown device, will act as a short-circu t ter minat on of the line 35. The said inductive loading will affect the electrical line len th when the line acts as a short-circuited line. The loading occurring at the loop 45 is sufficient in amount to make it imnractical'so to adjust the line'that when breakdown occurs in the breakdown device the line will behave as a short-circuited line of an electrical length of a cluarter-wave. Such an arrangement would'reouire the loop 45 to be placed much too close to the line 30 for convenience of construction. The line '35 is, therefore, designed so that when breakdown occurs in the associatedbreakdown device, the line 35 acts as a short-circuited transm ssion line of an electrical length of of a wave length.

At the junction of the lines 33 and 35, during conditions of electrical breakdown the. breakdown deviceassociated with the loop 45. the-r willbe two structures which contribute frequency-sensitivity which it would be advanta eous to count ract by a suitable transformer structure n accordance with the principles of this invention. These two structures are the supporting stub 4i! and the short-circuited. line 35, the latter contributing a greater portion of'frequency-sensitivact this frequency-sensitivity in accordancewith the present invention; a sleeve isprovided upon the conductor 3! or a length equal to a.half wave length for a frequency approximately in the middle of the desired transmission band and symmetrically disposedabout the junction of the lines 3i! and 35. This sleeve is shown at 41. Because of the greater amount of frequency-sensitivity in the lines 35 and 45, as compared with the two stubs and 25 of Fig. 13 or, a fortiori, the single stub 8 of Fig. l, the sleeve 4'! will generally be of a greater thickness than the sleeve 2! of Fig. 13 and will conse uently have a greater th ckness than the sleeve l3of Fig. l.

The branch line 35' is provided with an additional quarter-wave transformer formed by the sleeve-like enlargement d8 of the conductor 36. The matching transformer sleeve 43 is necessary to suppement the half portion of the sleeve 4'! which lies in the path of transmission around. the corner. The sleeve 36 may be made slightly thicker than the'sleeve 4'! on account of the fact that transmission around the corner of a T-junction is ordinarily accompanied by some reflection unle s those reflections are matched out by a transformer as more fully explained in connection with Fig. 15 in which the matching transformer 55 corresponds to the sleeve transformer i as anon-resonant transmission line, for instance,

in order to conduct a received signal from the transmission line 36 into the transmission line 35 and then through the electrical breakdown device (not shown), which during conditions of reception will not be broken down, but will pass signals from its input coupling to its output coup'ing, and finally to a receiver, it then becomes important to obtain a good degree of energy transfer between the transmission line and the transmission line 35. The sleeve 48 then functions to provide such energy transfer. The sleeve 48 is preferably provided with a diameter slightly larger than the diameter of the sleeve 41. Its length is governed by the same principle, substantially, as the length of the sleeve 55 as described more fully below, and the illustrative dimensions there given in connection with the latter may be applied to the sleeve 48 of Fig. 14. If the sleeve as is omitted, energy trans-v fer between the transmission line 38 and may be improved by increasing the size of the loop 45, but this has the disadvantage of making the loop so large as to bring it near the glass vacuum-maintaining envelope usually located in the electrical breakdowndevice and thereby causing corona to occur.

Figs. 15 and 18 show a form of structure in accordance with the present invention which may be readily converted from a straight through stub support of the general type shown in Fig.1

into a right angle stub support (which is 50 as shown at by dotted line. The conductors 55 and 56 of the main line 57, the length of the stub line 50 as closed by the plug 5|,

and the dimensions of the enlargement 53 which constitutes the transformer system of the device, may be, as in Fig. 1 and more particularly described in Table I. As will be presently more fully described, the inner conductor of the branch line 50 has a greater thickness than the corresponding inner conductor line of Fig. l, but, as pointed out above, the chief effect of this is to change slightly the characteristic admittance of the branch line 50 to a higher value. This change does not in this apparatus have any significant effect upon the behavior of the device, although theoretically it might vary the bandwidth slightly, so that with the arrangements-just described, which is to say with the branch line 5|) shortcircuited by the structure 5| and with the line 51 employed to transmit energy past the branch line and its associated transformer structure, the apparatus shown in Fig. 15 operates in the same manner as that previously described in connection with Figs. 1, 2; and 3.

, When it is desired to operate the apparatus shown in Figs. 15 and 16 as a right angle piece of transmission line with a stub support at the 'rightangle, the plug 5| is removed or omitted and instead a plug shown in dotted lines at 6| is inserted at a suitable location in the line 51 at one side of the junction of the branch line .50 and the main line 51. Although the plug 5| isshown-as a simple perforated disc and the plug 5| is shown as a flanged disc, it is to be understood that either type of plug may be used in either position. If the flanged disc is used, not only is there no change of diameter in the shortcircuited line, but the end of the thickened portion of the inner conductor of the line may be used for the purpose of locating the plug in the desired position by suitably adjusting the length of the flange on the plug. If a simple perforated disc plug such as the plug 6| is used, the effect of the change of diameter occurring in the shortcircuited line may be compensated by a small displacement of the position of the plug 6| from that which would otherwise be used. The necessary displacement can be estimated by suitable calculation and in any event can readily be de- ,.termined by experimental measurement. cause of the non-symmetry of the end effects occurring at the junction of the lines 50 and 51, the distance between the short-circuiting ter- .mination of the line 50 when it is used as a stub support and the axis of the conductor 55 is likely -t be different (generally somewhat longer) from the distance between the nearer wall of the plug 6| and the axis of the conductor 52, which is the inner conductor of the line 50. It may thus be convenient to provide a plug with two sleevevlike flanges, one on each face of the plug, these sleeve-like flanges being of different lengths, one suitable for locating the plug in the manner of the plug shown in dotted lines at 5| and the other suitable for locating the plug in the line 51 with reference to end of the transformer 58. When a plug such as the plug 6| has been provided at a suitable location in the line 51 as shown in Fig. 15, the portion of the line 51 between the plug BI and the junction of the lines .50 and 51 act as a stub support and the line is then adapted for transmission of radio frequency energy between the lines 51 and 5|] around the right-angle junction. For frequencies in the microwave right angle connection of the lines 51 and 50.

The position of the plug 6| is, therefore, adjusted so that the susceptance will be zero, which is possible, but there remains a real component (i. e. a conductance) of the admittance of the stub support. Thus it is desirable to provide in the.

branch line 50 not only a quarter-wave transformer to cooperate with half of the half-wave length transformer 58 to counteract the fref uency-sensitivity resulting from the susceptance of the stub support, but also an additional change in the relative diameters of the conductors of the line 50 for a length of an electrical quarter-wave length such as is adapted to compensate or match on the conductance occasioned "by the corner stub support. These two functions are combined into a single sleeve type transformer in the apparatus of Figs. 15 and 16. The conductor 52 is provided with a portion of enlarged diameter extending for an electrical quarter-wave length from the joint between the conductor 52 and the conductor 55. Such an enlargement may readily be provided by means of a sleeve mounted upon the conductor 52. In determining the physical length of the enlargement 65 which corresponds to an electrical quarter-wave length, account must be taken of the end effect resulting from the configuration of the. conductors of the lines 56 and 51. Illustrative values which have been found suitable for the physical dimensions in questions are listed below in Table II.

The thickness of the sleeve which produces the enlargement 65 is greater than the thickness of the sleeve which forms the enlargement 58 of the conductor 55, because of the additional effect which must be compensated for by the enlargement 65, as just described. The behavior of the apparatus shown in Figs. 15 and 16'when usedas a right angle stubsupport for transmission of energy through the lines 57 and 50 around the corner formed by their junction is illustrated in Figs. 1'7 and 18. In this illustration of the behavior of the arrangement, as in the case of Figs. 4, 5, 6, and 11, the capacitive effect of the discontinuities occurring at the ends of the transformers is omitted in order to simplify the illustrations of the behavior of the apparatus. This small additive effect may readily be taken into account in the manner illustrated in connection with Figs. '7, 8, and 9. Fig. 17,, then, illustrates the case for which the total length of the transformer 58 is a halfwave length and the total length ofthe transformer 65 is a quarter-wave length, and for which the stub support has a zero susceptance, although,

-as previously pointed out, it has a definite. nonzero conductance. Beginning the analysis at the bottom of the transformer 58, the effect of the half of the transformer 58 which lies below the axis of the branch line 59 may be represented by the semi-circular arc YOF. The effect of the stub support, which, as just pointed out, is a pure conductance, may then be represented by a horizontal line FG. The thickness of the sleeve which acts to form the transformer 65 is designed to be exactly .so much greater than the thickness of the sleeve which forms the transformer 58, that at this frequency the-admittance looking into the transformer 65 from the line 50 will appear tobe Y0, and consequently the effect of the transformer 65 is represented on'Fig. vl'lby the semi-circular arc GYo dr'awn about a point Y2 which point corresponds to the desired characteristic admittance of the transformer 65 and determines the transverse dimensions of the latter. At some lower frequency than that corresponding to the conditions of Fig. 17 a relation will be established such as that shown in Fig. 18. In this case the effect of the lower half of the transformer 58 is shown by the arc YoF. The stub support now has a susceptance component FH as well as a conductance component HG so that the resultant admittance of the stub is represented by the line FG. The effect of the'transformer 65 may then be represented by the arc G'Yo drawn, again about the point Y2 as center.

It is to be noted that the line F'G will be slightly unsymmetrically disposed about the axis W and further that thedifference between-the diameter of the two arcs will generally be such as to compensate for the ccnductance of the stub only in the neighborhood of the mid-band frequency for which the conditions were shown in Fig. 17. The variations of the admittance looking through the right angle stub structure arising from'this last mentioned circumstance will generally be extremely small within the range of frequencies usually desired. 1

The transition between the transformer 65 an the transformer 58 at the junction of these two structures may be carried out in various ways, the difference between the outer diameters of these two structures being so small-that the effect of varying the manner of the transition within reasonable limits is diflicult to measure. A preferred configuration for this joint is shown in Figs. 15 and 16. If desired, the circumferential edges at the junction end of the transformer 65 may be slightly rounded. Dimensions for a structure of the type shown in Figs. 15 and 16 which have been determined in accordance with the present invention and have been found practical are given in Table II.

Table m 7 [Mid-band wave length in air=l.]

Dimension Length Outer "diameter of conductors 52 and 55 0. 096 Inner diameter of conductors 53 and 56.; 0. 201 Length of sleeve 58 0.500 Outer diameter of sleeve 58 0.109 Length of sleeve 65 (dimension D on F and 16) 0. 293 Outer diameter of sleeve 65 0. 114 Length of stub for straight through line (dimension c on Figs. 15 and 16) 321 Length of stub for right angle line dimension d on Fig.

1 For flat disk form of plug:

Sections of transmission line for assembly into' radio frequency transmitting and receivin systems in a wide variety of possible physical con-' structions may be provided in the form of sections of coaxial conductor line having a structure such as that shown in Figs. 15 and 16 at each end of 1 the line. Either end of the sections may then be used'for a straight through connection or for a right angle connection. The arrangement of Figs. 15 and 16 simplifies the manufacturing problem by providing a structure which will serve either as a straight through stub support or as a right angle stub support, the' choice being determined and effected simply by'the location of a short-circuiting disk or plug.

In the foregoing description and explanation,

the most practical forms of the present invention," together with certain variations thereof, have been described and their behavior has been explained with the help of simplifiedtheoretical diagramsJ FQr the full understanding of the principles of the present invention from the; theoretical point of view and for a full apprecia-ftion of the scope of its application, furtherexamples 'should be considered, some of whichmay not at present have an immediate practical application because of the greater convenience of the preferred forms of the invention. Ac-'} cordingly, there are shown in Figs. 20-29 certain other I forms of the invention together with explanatory diagrams relating thereto.

It will be seenfrom the above description that the invention in principle consists in associating with a transmission line which is connectedwith a resonant structure that introduces frequencysensitivity, a resonant transformer so arrangedthat the frequency characteristic of the resonant transformer and the frequency.characteristic of the aforesaid resonant structure or elementwill substantially compensate each other overan appreciable' range in the neighborhood of: the resonance of the latter. The term resonant is used in the broad sense to include both series and -parallelresonance, the latter being sometimes referred to as antiresonance-. In gen-" eral, the arrangement in'question includes the provision of a resonant transformer such that at the frequency at which the said resonant structure is resonant (or anti-resonant, asthe casemay be), and atwhich it therefore does not introduce a finite non-zero susceptance,- the resonant transformer also has a zero net'effect so far as the production-of reflections in the transmission line is concerned, the transformer further beingsuch that it will exactly compensate the reflection-producing effect of the said resonant element at two other frequencies in the neighborhood of the said resonant frequency (except for a special case in which one of these; frequencies coincides with the middle.' resonant" frequency). The manner in which the reso-: nant transformer is to be designed and asso-. ciated with the resonant element in the case where the resonant element is substantially a parallel resonant circuit in shunt with a transmission line (for instance, a stub support) and where the transformer consists of suitably spaced= alterations inthe characteristic impedance of the transmission line, has been fully illustrated in the figures above referred to and in the; description relating thereto (except for a special case to be taken up presently in connection with- Figs. 28 and-29). The invention is, however, applicable to reducing the frequency-sensitivity which normally results when a series resonant circuit or its equivalent is inserted inseries with one of the conductors of a transmission line It also applies to arrangements making use of a resonant transformer of the double-stud type as well as to resonant transformers of the type involving changes inthe characteristic impedance of the transmission line. As a corollary, the invention also applies to the use of transformers?v of a typecombining the features of the double-M stub and change of characteristic impedance: types.

Fig.20 illustrates the use of a double-stub type of resonant transformer for counteracting the frequency-sensitivity ofa stub support 10 as sociated with a transmission line through which it is desired to transmit energy. -The= behavior of this arrangement is illustrated in Fig. 21. The stub support I0 corresponds totheaosaeer stub 8 ofFig. l. 7 On either'side of the supportin double-stub type which is for best results symmetrically disposed with respect to the stub support HI, of which it is desired to counteract the frequency-sensitivity. The stub H and 12 are not resonant at the frequency at which the stub 10 resonant In general, the stubs H and 12 should introduce a capacitive susceptance at their respective junctions withthe transmission line, 15 and the frequency at which the stub 10 is p'arallel-resonantLand they should be located at a distance from the stub lfl slightly less than one five, nine, "etc eighth-wave lengths, preferablyslightly less than a single eighth-wave length.. The. distance between the stubs ll and 12 will thusbe slightly less than an odd number of quarter-wave lengths. 7

i In order that the stubs H and 12 'may be capacitive and also not excessively frequencysensitive, they, are provided with open-circuit terminations. If the outer conductor of the stub is extended a relatively long distance beyond the end of the inner conductor, and is small enough in diameter, .the end may be either open or closed, as radiation will then be negligible in either case. The stubs ll and I2 constitute a special type of shuntreactance. Other shunt reactive arrangements might be used. If desired, short-circuited stubs ,of a length between a quarter-wave and a half-wave length may be. substituted for the shorter open-circuited .stubs (which should be less than a quarter-wave length long), with some increase frequency-sensitivity, however, and probably with some loss in overall band-width.

It will presently be pointed outin connection with Fig. 21Athat the stubs H and 12 may be replaced by inductive stubs located about a quarter-wave length away from the suitable location of the capacitive stubs ii and 12 respectively, without. substantially changing the behavior of the'apparatusexcept for the introduction of additionalfrequency-sensitivity in the transformer (and possible. reduction of band-width of the entire'device) on account of the greater length of transmission line 15 between the stubs of the double-stubv transformer. The substitution of inductiveforcapacitive stubs and the concomitant change of the spacing from each of said stubs to the. stub-m by a quarter-wave length is analogousto the substitution of the undercut transformers 22 and 23 of Fig. 12 for the sleeve transformer structure l3 of Fig. l.

The reasons underlying the choice of the characteristics of the stubs H and 12 and of the spacing betweenthem, and also the mode of operation of the arrangement shown in Fig. 20, may be explained in. connection with the diagram, Fig. 21. The point Yo indicates the characteristic admittance of, the transmission line I5. As previously pointed out, the stubs H and 12 are capacitive in effect over a range of frequencies in the neighborhood of the anti-resonant frequency of the stub' Hi. .The effect of the stub H at the said anti-resonant frequency may therefore be represented by the straight line YOLl. The distance-between the stub H and 12 is so arranged that at the said anti-resonant frequency the admittance looking to the left from the intersection of. the stub 12 and the line 15, disregarding the effect of. the stub 12, is represented by the point La which is to say that the length of transmis A grees as shown by the length of. the arc NlN2 sion linebetween the stub H and 12 is such as: to correspond to the number of electrical degrees In the previous represented by the arc LiLzIn. circle diagram it was not of particular importance to consider the distribution of electrical degrees about the are drawn on the diagram, because al-,

though the electrical degrees are not uniformly distributed about the arc (see Fig. 19), an arcof a circle drawn about a point on the real axis YY always includes electrical degrees between its intercepts on the real axis. A glance at Fig. 19 will show that the arc L1L2L3, although geometrically more than degrees, will amount to less than 90 electrical degrees, which is to saythat the length between either the stub H or the stub 12 and the stub ill should be somewhat less than an eighth-wave length (or, in general, somewhat less than one, five, nine, etc., eighth-wave lengths). Since the stub lflqis anti-resonant at the frequency just considered, it will not affect the diagramYoLiLaLaYo. The effect of the stub 12 is represented by the vertical line LsYo, so that at the frequency in question the transmission line is perfectly matched through the structure. It is to be noted that in this case the cir-. cular arcs belong to the family associated with Yo, the point representing the characteristic ade mittance of the transmission line, which is unchanged throughout.

' At some frequency lower than the anti-resonant frequency of the stub 10, the situation represented by the line YOM1M2M3M4Y0 will hold. At this lower frequency, the capacitive admittance of the stubs II and 12 will be less than that at the anti-resonant frequency of the stub 10, and will, therefore, be represented by the lines YOM], and M4Y0 respectively. The change in the admittance looking to the left from various points on the transmission line, 15 between the stubs H and 72 will then be represented by the arcs MlMZ and M3M4, which are shorter than the corresponding arcs L1L2 and LzLs on account of the lower frequency in thecase now being considered. The stub 10, however, will have an inductive effeet at this lower frequency, so that its efiect will be represented by theline M2M3, and it will thus be seen that there will be a frequency for which the line YOM1M2M3M4YO, bringing the admittance back to Yo at the intersection of the stub I2 and the line 15, will be representative. Likewise, there will be a frequency higher than the anti-resonant frequency of the stub iii for,

which the diagram YONlN2N3N4YO will represent the conditions in the apparatus, the susceptance of the stubs 'H and 12 now being greater as shown by the lines YoN1 and N4Yo, the effect of the intervening portion of the transmission line 15 being to introduce a greater number of electrical deand N3N4, which overlap in the portion N3N2, and the effect of the stub TE! now being capacitive as shown by the straight line N2N3.

The case in which each of the stubs H and '32 are replaced by an inductive stub located a quarter-wave length farther out from the stub 10, for instance the stub shown in dotted line at 73, a similar stub being substituted for the stub 72 on the other side of the stub 70, is illustrated in the diagram Fig. 21A (on the last sheet ofv drawings) by the fact that the arcs involved in the diagram are longer. The mid-band resonant frequency of the device is represented by the diagram The somewhat greater frequency-sensi-. tivity of the transformer arrangement is shown,

The effect of the stub 10, which appears at the point L'z, is zero, this being the anti-resonant frequency of the stub It. The are LiL'z and L'2L'3 overlap in a portion of LiL'z. It will be seen from the length of the arc L'1L'2L'3, and from a reference to Fig. 19, that the distance between the inductive stubs here considered will be Slightly greater than threequarters of a wave length, so that the distance between the stubs 1| and 1 3 on Fig. 20 should be more than a quarter-wave length instead of a. quarter-wave length as previously suggested. This is, however, a minor adjustment, and its extent may be readily calculated with the help of circle diagrams of the type of Fig. 21 and Fig. 21A. For a frequency lower than the middle resonant frequency there will be another resonant transmission frequency of the device indicated by the line YOM1M2M3M4Yo. The arcs in question now have a smaller number of electrical degrees, while the lines representing the inductive susceptance of the stubs of the double-stub transformer have a smaller magnitude. The effect of the stub is inductive and is shown by the line M'zMs. At a frequency higher than the aforesaid middle resonant frequency of the device there will be another resonant frequency of transmission as illustrated by the line Y'oN'1N2N'3N4Y'0. The effect of the transformer stub is now to introduce a susceptance of greater absolute magnitude, while the arcs in question are longer in terms of electrical degrees and the effect of the stub 18 is capacitive as shown by the line N '2N'3.

The exact length of the stubs H and 12, and, in the case of Fig. 21A, of the stub 13 of Fig. 20, is not critical so long as the stubs H and 12 are capacitive in the desired range and, in the other case, so long as the stub 13 is inductive in the desired range. The magnitude of the susceptance provided by the stub at the middle transmission frequency determines the radius of the arc L1L2 of Fig. 21 and the arc LiLz' of Fig. 21A, so that it is in a sense analogous to the magnitude in the change of characteristic impedance ef-' fected by the sleeve I3 of Fig. l or by the undercut portions 22 and 23 of Fig. 12. Just as the transformers of Figs. 1 and 12 may be'adjusted for various degrees of compensating frequencysensitivity by varying the proportional, increase or decrease in the diameter of the conductor 6, theamount of compensating frequency-sensitivity provided by the double-stub transformer of the type generally indicated in Fig. 20 may be adjusted by proper choice of the length of the stub H and 12 and, in the case of inductive stubs, of the length of the stub13 and of its mate. Since the stub reactance depends upon the characteristic impedance of the stub as well as upon the length of the stub (as mentionedin the case of the supporting stub 8 of Fig. 1), the selection of the characteristic impedance may also serve to control the frequency characteristic of the devices here described. The desired stub length for counteracting the frequency-sensitivity of a given anti-resonant element such' as the stub 10 can be calculated graphically by means of circle diagrams of the type illustrated herein in accordance with the herein outlined method.

Fig. 22 illustrates the application of the invention for reducing or compensating the frequencysensitivity introduced by a series resonant element which appears in series with one of the conductors of a transmission line. The transmission line is illustrated at 80, and the series resonant: element is represented by a resonator 8| 22": coupled to the'tra'nsmission-line by means of a hole'or slot 82' preferably elongated circumferentially with respect to the axis of the transmission line 88. The hole or slot 82 will thus interrupt currents irr the transmission line 80 and an electric field will appear across it which is adapted to excite the resonator 8|. The effect of the resonator 8| thus coupled into the transmission line 80 may be regarded as the interposition in series with the outer conductor of the transmission line 88 of a series resonant circuit, the resonant frequency of which is substantially the resonant frequency of the resonator 8|. In order' to compensate for the frequency-sensitivity of the resonator 8| for the purpose of improving the transmission characteristic of the transmission line 88, the diameter of the inner conductor of the transmission line 80 is reduced, as shown at 83, for a distance of substantially a half-wave length at the resonant frequency of the resonator 8|, symmetrically disposed with respect to the coupling aperture 82, so that this section of transmission line having an inner conductor of reduced diameter may be regarded as a half-wave undercut resonant transformer, or as a pair of quarter-wave undercut resonant transformers; with their ends joined. The behavior of the ar-' rangement of Fig. 22 is more conveniently illustrated upon an impedance diagram rather than upon an admittance diagram, the admittance diagram having been more convenient in the previous cases dealing with parallel resonance andshunt susceptance. The impedance diagram is essentially the same as the admittancediagram,

it being understood that impedance is the recip rocal of admittance, and that both diagrams represent complex quantities. The impedance diagram, like the admittance diagram,-hasthe general form shown in Fig. 19.

The behavior of the apparatus illustrated in Fig. 22 is shown by the diagram Figs. 22A, 22B, and 22C. The real axis in each of these diagrams is represented by the line ZZ. represents the characteristic impedance of the transmission line 88. The point Z1 represents the characteristic impedance of that particular,

portion of the transmission line 80 in which the inner conductor has a reduced diameter as shown at 83. Following the previously employed procedure of analysis, the effect of the first half of the undercut section of transmission line will be represented, at the middle resonant frequency of the structure, by the upper arc ZoZ2. The resonator 8|, the effect of which enters at the point Z2, here has zero effect (assuming losses to be negligible) ,being at resonance, and therefore adds nothing to the diagram. The effect of,

the rest of the undercut transformer section is then represented by the lower arc Z2Zo. It will be seen that each of these arcs correspond to ninety electrical degrees and that the total length of the transformer is therefore electrical degrees or a half-wave length. End effects at the extremities of the transformer section are neglected inthis analysis as in most previous cases; they may be adjusted for, if desired, as previously explained in connection with Figs. 1, 7, 8 and 9, such. end effects being gen-. erally the introduction of a slight amount of capacitance at the ends of the transformer section, whether the transformer is of the sleevetype or of the undercut type.

At a frequency lower thanthat considered in.

Fig. 22A, the arcs representing the effect of the two halves of the.undercut.transformer sec- The point Z0 2'3" tion will be shorter as shown in Fig. 2213. The impedance presented in "series with the transmission line by the resonator 8! will then be capacitive, as indicated by the line Z3Z4 (this line is downwardly'directed, since on the impedance diagram inductance is represented upwards, whereas on the admittance diagram capacitance is'represented upwards). Fig. 22B represents the lower resonant transmission frequency of the device of Fig, 22.

The upper resonant transmission frequency of the device of Fig. 22 is illustrated by the'diagram, Fig. 220. In this case the arc corresponding to the effect of the two halves of the transformer are longer than 180 degrees (longer than 90 electrical degrees) each and overlap over the portion Z'sZs. .The effect of the resonator 8i, which is inductive, is represented by the straight line ZsZs.

Fig. 23 illustrates the use of a double-stub type of transformer for reducing or compensating for the frequency-sensitivity introduced'by a series resonant element inserted in series with one of the conductors of a transmission line. The transmission line is again shown at 80, and the series resonant element is again represented by the resonator '81 coupled to the transmission line 89 by a hole or slot 82. The transformer provided in accordance with the present invention is 'in' this case a transformer of the double-stub type comprising the stubs 84 and 85. Just as in Fig. .22, where a series resonant element in series with the line wa'salso involved, an undercut type of transformer was used, whereas in Fig. 1

where a parallel resonant element in shunt with the line was involved a sleeve type of transformer was used, soin the present case, the stubs 34 and 85, for thefshortest type of transformer, should be inductive, in contrast to the use of capacitive stubs in the, arrangement of Fig. 20. As will appear froma consideration of Fig. 24, for the shortest transformer the stubs 8 and 85 should be separated by slightly less than a quarter-Wave length of the transmission line 30. As in the case of Fig. 20, an arrangement employing the other type of stub, in this case capacitive stubs,

can be constructed. which is substantially equiv-- alent except for the introduction 'ofsomewha't more frequency-sensitivity in the transformer because of the increased amount of the transmission line 80 included in the double-stub transformer,

The exact counterpart of Fig. 20 for counteracting the frequency-sensitivity of the resonator 8| in Fig. 23 would comprise additional series reactances inserted in the transmission line on either side of the resonator 81, in which case the impedance diagram would look, substantially exactly the same as the admittance diagram shown in Fig. 21. Although the principle of the invention may be applied to transformers including a pair of series r'eactances inserted in a line at a suitable distance from each other so as to constitute a resonanttransformer, it is inconvenient, at least so far as the present state of the art is concerned, to insert structures which will be effectively series rcactances inserted: in a transmission line of ordinary construction, so that for a more practical illustration there is shown inFig. 23 the use of shunt reactances,

namely the stubs 8d and 85. The impedance diagram now becomes more complicated because both shunt and series reactances are to be considered.

The impedance diagram is'shown at Fig. 24, the line -ZZ being the real axis and the origin appearing at 0. Zn represents the characteristic impedance of the transmission line 8t. For the purpose of this diagram it. is assumed that the spacing between the stubs 84 and 85 is of the order of a single quarter-wave length. It is to be understood that instead of the stubs 34 or $5 spaced, as will be seen, by slightly more than a quarter-wave length, a pair of capacitive stubs.

Since Fig. '24 is an impedance diagram and since the impedance of the stubs 84 and 85 is in parallel with the line 80, the resultant impedance of the parallel combination, as seen at the location of the stub, cannot be represented by a point on a vertical line passing through Zn. The locus of the resultant impedances, instead of being a vertical line through Z0, is a circle passing through Z0 and the origin, and having its center on the real axis, the circle in question being shown in dashed lines on Fig. 24. On this circle the origin corresponds tov zero shunt impedance or infinite shunt susceptance, and the point Z0 corresponds to infinite shunt impedance or 'zero' shunt susceptance;' Thus the points corresponding to higher values of impedance of the stub will li'e closer to Z0 than points for lower values of impedance.

For the mid-band resonant frequency the situation will be represented by the line zbaiwzas zo, the lines Zuar and asZo representing the effect of the stubs 8d and 35 respectively, whereas the circular arc represents the effect of the intervening length of transmission line. For a lower fre-,

quency than that just considered the effect of the V stub 84 may be represented by Z051, the effect of the first half of the transmission line lying between the stubs by [31b2, the effector the inter- I posed series reactance of the resonator 8| by the straight line ,8253 (the reactance being capacitive), the effect of the remainder of the trans- 1 mission line included between 84 and 85 being represented by the are 5354 and the effect of the stub 85 being represented by the .line fiiZo. In a similar manner there will be another frequency lower than the first-mentioned frequency which.

may be represented by the diagram ZoywzvswZo.

It will be noted from the diagram Z0a1a2a3Z0 and' from a. construction of the dashed circle onto Fig. 19 (not shown) that the arc a1a2a3 includes.

necessarily somewhat more than electrical degrees, so that the spacing between the stubs 84 and 85 should .not be exactly a quarter-wave length but slightly more than such. It will also be seen that as the frequency decreases the point or is pulled back not only by the reduced length the electrical degrees of theatre 5152 but also by the increase in the electrical degrees in the,

portion of the circle pics intercepted by the angle InZQZ'. It may similarly be observed with regard to Fig. 21 that the point M2 is pulled to the left as the frequency 'decreases not only by the a reduced length of the arc M1M2, but also by the change in scale in'electri'cal degrees as one progresses toward circles of smaller radius (see Fig. i 19). These factors, however, do not prevent transformer structure of the double-stub typeof being valuable for counteracting the frequency-' sensitivity of elements associated with a transmission line and may improve the quality of compensation in some cases.

If desired, the arrangement of Figs. 1 and 20 or the arrangement of Figs. 22 and 23 may be combined within the principles of the present invention. Thus in the first case the portion of the transmission line 15 lying between the stubs II and 12 might be arranged to have a higher characteristic admittance than the rest of the transmission line 15, as by increasing the diameter of the inner conductor of the transmission line or reducing the diameter of the outer conductor of the transmission line. In the second case just mentioned, referring to Fig. 23, the portion of the transmission line 80 between the stubs 84 and 85 might be arranged to have a higher characteristic impedance than the rest of the transmission line, as by reducing the diameter of the inner conductor or increasing the diameter of the outer conductor of the said transmission line.

If the arrangements of Figs. 20 and 1 are combined as above suggested, so that the transformer arrangement comprises a sleeve type thickening of the inner conductor of the transmission line having at each end a shunt capacitively reactive stub, the circle diagram for the middle resonant frequency will correspond to Fig. 7, except that the capacitive stubs may be expected to exhibit considerably greater susceptance than that represented by the lines YoP and QYo. The family of circle diagrams will resemble that shown in Fig. 21 except that the arcs will belong to the family of circles about a point Y1, to the right of Y0, instead of the family of circles about Yo as in Fig. 21. It will be seen that for the least frequency-sensitive transformer of this general type the total transformer length will be between slightly less than a quarter-wave length (Fig. 20) and a. half-wave length (Fig. 1). The use of loading capacitances in this manner may be useful in cases where frequency-compensation by the method of Fig. 1 entirely would involve risk of electrical breakdown on account of reduced mechanical clearances in the line.

Figs. 25 and 2'7 show typical applications of the present invention to systems employing hollow pipe wave guides instead of coaxial conductor transmission lines. In Fig. 25 the rectangular pipe 90 represents the wave guide adapted to transmit waves in the Hm mode, sometimes referred to as the TEn,1 mode, and might, for instance, be used to connect a transmitter to an antenna. The pipe 9| is a similar wave guide pipe forming a junction with the pipe 90 and might conveniently be used to connect to a receiver for operating in connection with an antenna common to both transmitter and receiver. When the pipes 90 and 9| are used as suggested, it is advantageous to provide in the pipe 9| a protective electrical breakdown device which will cause a short circuit to appear in the pipe 9| when the transmitter is operated. The said electrical breakdown device (not shown) is to be located in the pipe 9| in such a position that the said short circuit is caused to appear at substantially a half-wave length from the mouth of the pipe 9| where it joins the pipe 90 so that substantially no energy will be caused to be reflected back towards the transmitter during transmitter operation, and a maximum of energy may be transmitted along the pipe 90 past the junction. The shaded rectangle 92 represents a short circuit across the wave guide 9| such as 26 might be caused byan electrical breakdown 'de-' vice located as aforesaid. It will be seen that the presence of the branch pipe 9|, even when short circuited even as aforesaid, will introduce frequency-sensitivity into the transmission characteristic of the pipe during transmitter operation, because zero reflection towards the transmitter from the short-circuited branch holds only for a particular wave length. The present invention may be applied to reduce or counteract the said frequency-sensitivity as follows. Thebranch pipe 9| as shown in Fig. '25 and short-circuited at the location 92 constitute essentially a series resonant circuit interposed in series with the'upper wall of the wave guide 99 which may be regarded as a sort of transmission line. The mouth of the pipe 9| will inter;- cept longitudinal currents in the upperfwall of the pipe 90, so that an electrical field will occur across the said mouth and the s'hort-circuited branch pipe will act in a manner similar to the mode of operation of the resonator 8| in Figs. 22 and 23. The frequency-sensitivity introduced'by the short-'circuited branch pipe 9| may, in accordance with the present invention, be counteracted by providing a resonant transformer of the proper kind in the pipe 90, either by changing the dimensions of the pipe, particularly the narrower dimension, thereby changing what may be termed the characteristic impedance of the pipe then regarded as a transmission element,'or by inserting structures providing susceptive loading and therefore acting like the stubs H or 13 of Fig. 20. In Fig. 25 the latter methodjis shown, inductive susceptance being provided at suitably located points on each side of the 'wave' guide junction by the pairs of curtains 93; 93d and 94a.

These curtains are sometimes"considered'as' a type of iris diaphragm. The behavior of the structure is illustratedin Fig. 26, which is substantially the same as Fig. 24. Thusthe middle resonant frequency may be arranged to corre'- spend with the situation shown by thelines Z0F1FE2F3Z0. The effect of the curtain pairs 93, 93a and 94, 94a are then represented respectively by'th'e lines ZoF1 and FsZo. The effect of the short circuited'branch pipe, which takes place at F2, is zero because the frequency considered is the resonant frequency for which the length of the short-circuited branch is a half-wave length from the position of the short circuit to the mouth of the pipe. As in the case of Fig. 23, the distance between the inductive susceptance loading 93, 93a and 94, 94c should beslightly more than a quarter-wave length. Instead of "quarter-wave length spacing, a spacing slightly more than five-quarters of a wavelength might 'be used, although this would introduce slightly more frequency-sensitivity in the transformer arrangement. Likewise capacitive loading could be used instead of inductive loading at positions slightly less than a quarter-wave length farther out from the junction than the positions illustrated in Fig. 25 for the elements 93, 93d, 94 and 94a. At some lower frequency thesituation will be that represented by the line ZoG1GzGcG4Z0. At this lower frequency the short-circuited branch pipe is slightly less than a half-Wave length long, so'that it has a capacitive effect and is therefore represented by the downwardly directed vertical line G2G3. At the sarne time the spacing between the elements 93 and 94 is shortened in terms of electrical degrees so that its'efiec't 27 maybe represented by the arcs G1G2 and G3G4 The impedance resulting from the curtain pairs 93;" 93aand 94-, 940; respectively, being lower desired, an additional pair of curtain-s 95,

85a may be-provided in the wave guide 9| as showninFig. 25 to improve the impedance match around'the wave guide corner at the junction, whenthetransmitter previously referred to is not in operation and the short-circuit at the position .QZ-istherefore removed. Such pair of curtains .95; 95wwould a general way correspond to the sleeve type matching transformers 65 of Fig. and 48 of Fig. 14-. It may be pointed out that when. the junctionarrangement shown in Fig.

is used for purposes of reception, with energy being led around the wave guide corner instead of straight through past the junction, that branch of the wave guide 90 which is not used during reception for the transmission of energyis pref- 'erably adjusted in length or otherwise arranged toreflectienergya consequently, it will introduce frequency-sensitivity." The transformer arrangement effectively constituted by the curtain pairs 93, 93a and 95, 95a in such case tends to reduce .such frequency-sensitivity in the same manner that frequency-sensitivity is reduced in the apparatus of Fig. 15 when it is used as a "corner type stub summit with the plug Bl in position and the'plug 5| out of position.

"It-is to be noted that in pipe wave guide structures such as that illustrated. in Fig. 25 the wave length of the oscillations in the guide is generally" longer by a substantial amount than the wavelength of oscillations of the same frequency in free space or in an air-insulated coaxial-conductor transmission line. The dimensions given in terms of wave lengths in connection with 25 are therefore to be referred to the wave length of the oscillations in the wave guide and not to be free space wavelength. 'Since the wavelength in a rectangular wave guide for the Hod mode: depends only upon the broader dimension of the wave guide cross section, the narrower dimension of said cross section may be varied to change what corresponds to the characteristic impedance of the wave guide without .at the same time changing the wave length in the wave guide.

If'the short circuit represented by the shaded area 92 could be made to occur at the mouth of the wave guide 9|, there would be substantially no problemof frequency-sensitivity, but in practice it is-often inconvenient so to locate the electrical breakdown discharge apparatus associated with the wave guide 9|.

. The form of junction shown in Fig. 25 is known as an electric plane junction. A "magnetic plane junction is shownin Fig. 27. The wave guide which goes straight through the junction is shown at 9B, the branch wave guide 91 open ing into one of the narrow walls ofthe wave guide 96. The shaded projected rectangle 98 indicates a short-circuit in the samemanner as indicated by the shaded area 92. The mouth of the wave guide 91, interrupting as it does the narrower wall of the wave guide 96, will not intercept any of the longitudinal current of the inner surfaces of the walls of the wave guide =98. which flow on thebroader walls of the wave 28 guide only, but will instead intercept the lateral current flowing across the narrower wall (vertically with regards; to Fig. 27 When the wave guide '96 is regarded as a transmission line, the central parts of. the broader walls may be regarded as the conductors. It will therefore appear that the short-circuited branch pipe 91 is not. in series with the wave guide when regarded as a. transmission line but is essentially a parallel resonant circuit in shunt with the wave guide so regarded. The wave guide usually measures aboutv one-half wave length across in its broad dimension, so that a series resonant circuit at the narrow wall will appear as a parallel resonant circuit at the center. The short-circuited magnetic plane junction of Fig. 27- may therefore be treated in the same manner as the stub support la in the line 75 shownin Fig. 20 (or indeed, as the stub support 8 in the line 5 on Fig. 1). Frequency-sensitivity introduced by the short-circuited branch may therefore be counteracted by capacitive loads in shunt with the line spaced slightly less than one,v five, nine, etc., eighthwave lengths from the center of the junction or by inductive loads spaced in accordance with Fig. 21A. Or, following the procedure of Fig. 1, the narrow dimension of the Wave guide 95 might be reduced for a length of an odd number of half-wave lengths. In each caseI prefer to dispose the transformer arrangement symmetricallv about the junction.

In Fig. 27, the transformer arrangement is constituted by the pairs of curtains 99, 99a and H19, llilla, each pair constituting a capacitive load (an alternative arrangement of inductive loads being shown in dotted lines at Nil). Because the branch pipe 91 is about a half-wave length wide, spacing of a half-wave length or less between the susceptive loads constituting the transformer would be difficult to calculate because of the likelihood of end effects on account of the presence of the junction. It is probable that end effects would not seriously interfere with a half-wave length transformer of the type produced by reducing the narrow dimension of the pipe 96 for a half-wave length, however.

The capacitive curtain pairs 99., 99a and mo, mild are. shown in Fig. 2'7 separated by slightly less than five-quarters of a wavelength. A shorter transformer, hence less frequency-sensitive, may be formed by the inductive curtain Hi! instead of the capacitive curtains 99, 99a, I00, and 100a. The curtains In! are slightly more than three-fourths-wave length apart. They involve less risk of voltage breakdown than the capacitive curtains. Capacitive elements that do not increase breakdown hazards may be provided by suitable branch pipes, but the use of inductive elements is usually more convenient. It may be noted here in passing that the type of junction shown in Fig. 25 is in practice usually preferred to the type of junction shown in Fig. 27 because of the better match around the corner when it is attempted to transmit energy in or out of the branch pipe, so that less elaborate matching arrangements. are necessary for the best transfer of energy around the corner; indeed, in some cases the match is good enough to permit dispensing with special matching arrangements directed solely towards improving the energy transfer around the corner.

In the forms of the invention heretofore considered the compensating transformer arrangement for reducing the frequency-sensitivity of aresonant or anti-resonant element associated with a transmission line, or, more generally, a

wave guide (a two-conductor transmission line being a special case of a wave guide), has been symmetrically disposed with respect to the said resonant or anti-resonant element, or, at least, part of the transformer arrangement has been located on each side of the said element. Such disposition is necessary in order that the combined structure may have three resonant transmission frequencies within the pass band as heretofore explained and described. An unsymmetrically disposed transformer arrangement may provide a certainamount of reduction of frequency-sensitivity without, however, giving the effect of a band-pass filter which is obtained with the at least partially balanced arrangements herein described. The nature and extent of the effect of providing completely unsymmetrical resonant transformer in association with a resonant element associated with a transmission line is illustrated in Fig. 28 and in the explanatory diagrams, Figs. 28A, 28B and 28C.

Fig. 28 shows a transmission line I Hi provided with a supporting stub Ill substantially similar to the stub 8 of Fig. l. A half-wave matching transformer of the undercut type is provided by reducing the diameter of the inner con- .ductor of the line ID for substantially a halfwave length corresponding to the frequency at which the stub III is anti-resonant, the reduction in the diameter of the inner conductor being shown on Fig. 28 at H2. The portion of line I ID in which the inner conductor has a reduced diameter extends from the junction with the stub III to one side for the distance of approximately one-half-wave length. The behavior of such a structure is illustrated in Figs. 28A, 28B and 28C. Fig. 28A represents the condition when the frequency is equal to the antiresonant frequency for the stub, at which frequency the undercut transformer has the length of a half-wave length. The stub then has zero effect and the effect of the transformer section of line is represented by the circular are beginning at Y and going clockwise and down- .Ward from Y0, since the characteristic admittance Y1 of the portion of line having. an' inner conductor of reducedv diameter is lower than is less than 180 electrical degrees so that. the 1 1 are YzYa is less than a full circle. For one particular frequency the point Y3 will lie on. the real axis YY, but it will be at some other point than the point Y0.

Fig. 280 shows the condition at frequencies ;1

higher than that corresponding to Fig. 28A. .The effect of the stub is then capacitive and may be represented by the line vYoY4. The transformer has an electrical length greater-than 180 electrical degrees so that the circular arc representing the effector the said transformer will be longer than a full circle. For some particular frequency the other end of the said are will lie on the real axis W at a point Y5, but such point will again be some point other than the point Yo. Thus at .all frequencies other than that corresponding to 'Fig. 28A, there will be I some reflection caused by the structureshown in Fig.28 in the transmission line M0,: but it will be. seen that for frequencies in the neighborhead of the frequency shown in Fig. 28A, which will be true for the entire included range of frequency as well as for some frequencies outside the range included between the frequency corresponding to the diagram 28B and the frequency corresponding to the diagram 280.

Another example'of an unsymmetrical transformer arrangement producing some compensation of the frequency-sensitivity of a stub support, although not as effective compensation as in the case of the symmetrical transformer arrangements herein described, is shownin Fig. 29. This arrangement is more closely related to the principal forms of the present invention than that just described because the arrangement of Fig. 29 can be constructed so as to provide more than one resonant frequency of transmissionin this case two such frequencies. The behavior of the device is illustrated in Fig. 30. Fig-29 shows a transmission line H5 having a right-angle bend supported by a stub line I [6. As previously pointed out in connection with Fig. 15, such a right-angle stub-supported corner presents a mismatch which, when referred to the rightangle junction, is composed almost entirely of a component along the real axis (referring to the change in admittance from the characteristic admittance of the transmission line). mismatch may be compensated by a quarterwave length matching transformer adapted to cancel out the reflections occurring at the juncwave length away from the junction. I have found that both of the arrangements just mentioned will result in some decrease of the frequency-sensitivity normally to be expected from the stub H6. I have further found that it is somewhat preferable to employ an undercut" transformer having a length either more or less than a quarter-wave length, which requires a readjustment of the spacing between the end of the transformer and the junction, as can readily be ascertained from circle diagrams. Specifically, in order to provide conveniently for a broadband transmission characteristic exhibiting two resonant frequencies of transmission, I prefer the arrangement shown in Fig. 29 in which the conductor if! is undercut as at I I9 for a length of somewhat more than a quarter-wave length at midband frequency (for example, about0.3 wave length) and located with its upper end slightly less than a quarter-wave length at midband frequency (about 0.22 wave length, for example) from the center of the right angle junction. Incidentally, it seems'to be impossible, or at least impractical, to provide band-broadening with a matchingtransformer associated with the conductor N8, the stub arrangement in Fig. 29 being unsymmetrical.

The mode of operation of the arrangement of Such 7, 

